Will my three year old grow out of his food allergies?

Maybe. Peanut and tree nut allergies are less likely to wane over time, but a small percentage of patients will lose their sensitivity eventually. Eggs, milk, wheat, and soy allergy are more likely to go away.
It depends. It depends on the type of food allergy your 3 year old has. If it is milk or egg allergy then the chances are good that he or she will outgrow it. If it is peanut allergy then the answer is no, he or she will probably not outgrow that allergy.
Hopefully. Children have a good chance of outgrowing their food allergies, but it depends on the type of food, the history of reaction, the level of sensitivity, and frequency of accidental exposure. Some food allergies are more likely to be outgrown than others. Most childreen outgrow milk and egg allergies, although it may take years. Only 15-20% of peanut and tree nut allergic individuals outgrow.
Most likely. . Depends on which food he is allergic to the chances of him growing out of them will vary. For most foods, he should be able to grow out of them. Seafood and peanuts usually are the ones that tend to stay with you, however, children can grow out of these as well.